`int_(-pi/2)^(pi/2) sin^7x dx`

int_(-pi/2)^(pi/2) sin^(7) x dx

int_(-pi//2)^(pi//2)sin^(7)x dx=

Evaluate: int_(-pi//2)^(pi//2)sin^2x\ dx

int_(-pi/2)^(pi/2) sin^(2) x dx

int_(-pi/2)^(pi/2)sin^(9) x dx

Evaluate : int_(-pi//2)^(pi//2) |sin x|dx

Evaluate: int_(-pi/2)^( pi/2)|sin x|dx

int_(-pi//2)^(pi//2) sin^(2)x cos^(2) x(sin xcos x)dx=

Prove that : (i) int_(-pi)^(pi) x^(10) sin^(7) x dx =0 (ii) int_(-pi)^(pi) (sin^(25) x+x^(75))dx=0 (iii) int_(-pi)^(pi) e^(|x|) dx= 2 (e-1) (iv) int_(-pi//2)^(pi//2) sin^(9) x dx =0